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Jun
22
answered Why is this relation irreflexive? And how can I prove it?
Jun
20
answered Is this polynomial irreducible in $\mathbb{Q}$?
Jun
20
comment Probability with coin toss
The problem statement is unrealistic insofar as politicions voting behaviour is not determined by them tossing a coin, but rather by otthers tossing many coins at them :)
Jun
20
comment Prove that this transformation is a reflection
Yes, that's fine with me. However, it is not even necessary to use a base and argue with matrices ...
Jun
19
answered Proof about isometries
Jun
19
revised Proof about isometries
added 62 characters in body
Jun
19
comment Vertices that create a convex quadrilateral
@Epic Alomost, but not quite. If you choose $AB$ and $BC$ out of $ABC\ldots Z$, say. there are several more solutions than just $ABCD$ and $ABCZ$ (which are also counted under $(AB,CD)$ and $(ZA, BC)$. There are also $ABCE, ABCF,\ldots , ABCY$.
Jun
19
comment Prove that this transformation is a reflection
@DanielFischer He says: unit vector
Jun
19
answered Prove that this transformation is a reflection
Jun
19
revised $T: V \rightarrow V$ a linear transformation such that $T^2 = I$ and $H_1= \{v \in V | T(v) = v\}\ $ and $H_2= \{v \in V|T(v) = -v\}\ $
The intersction is the zero-dimensional space, not the empty set
Jun
19
comment $T: V \rightarrow V$ a linear transformation such that $T^2 = I$ and $H_1= \{v \in V | T(v) = v\}\ $ and $H_2= \{v \in V|T(v) = -v\}\ $
@surb Let $k$ be any field of characteristic $2$, let $V$ be any nontrivial $k$-space and let $T$ be the identity. Then $H_1\cap H_2=V\ne 0$. The crucial step in your answer is: $v=-v\implies v=0$. This uses that the characteristic is $\ne 2$.
Jun
19
answered Showing holomorphic function is constant via conformal map
Jun
19
comment Validity of a trigonometric proof that $2 = 0$.
What is $\tan 90^\circ$? It is not a real number ...
Jun
19
answered If $A$, $B$, $A-B$ and $I+A$ are invertible $n×n$ matrices then prove the following
Jun
18
answered show that $f'(x)=0$
Jun
18
answered Necessary condition (s) for the divisibility relation $(2a+b) \mid (a+b)^{n}$
Jun
18
answered $T: V \rightarrow V$ a linear transformation such that $T^2 = I$ and $H_1= \{v \in V | T(v) = v\}\ $ and $H_2= \{v \in V|T(v) = -v\}\ $
Jun
18
comment $T: V \rightarrow V$ a linear transformation such that $T^2 = I$ and $H_1= \{v \in V | T(v) = v\}\ $ and $H_2= \{v \in V|T(v) = -v\}\ $
The statement is not necessarily true. Are there any additional assumptions about the ground field?
Jun
13
comment Matching gender expectation
Well, we were givem that $x,y$ are large, so I used $x-1\approx x$ (and so did Eric)
Jun
13
answered Matching gender expectation